Self-Duality and a Hall-Insulator Phase Near the Superconductor-to-Insulator Transition in Indium-Oxide Films

We combine measurements of the longitudinal (ρ_xx) and Hall (ρ_xy) resistivities of disordered 2D amorphous indium-oxide films to study the magnetic-field tuned superconductor-to-insulator transition (H-SIT) in the T → 0 limit. At the critical field, H_c, the full resistivity tensor is T independent with ρ_xx(H_c) = h/4e² and ρ_xy(H_c) = 0 within experimental uncertainty in all films (i.e., these appear to be "universal" values); this is strongly suggestive that there is a particle. vortex self-duality at H = H_c. The transition separates the (presumably) superconducting state at H < H_c from a "Hall-insulator" phase in which ρ_xx → ∞ as T → 0 whereas ρ_xy approaches a nonzero value smaller than its "classical value" H/nec; i.e., 0<ρ_xy < H/nec. A still higher characteristic magnetic field, H^z.ast;_c > H_c, at which the Hall resistance is T independent and roughly equal to its classical value, ρ_xy ≈ H/nec, marks an additional crossover to a high-field regime (probably to a Fermi insulator) in which ρ_xy > H/nec and possibly diverges as T → 0. We also highlight a profound analogy between the H-SIT and quantum-Hall liquid-to-insulator transitions (QHIT).